Question: Solve for $x$ and $y$ using elimination. ${-6x-3y = -36}$ ${5x+3y = 35}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-6x-3y = -36}\thinspace$ to find $y$ ${-6}{(1)}{ - 3y = -36}$ $-6-3y = -36$ $-6{+6} - 3y = -36{+6}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {5x+3y = 35}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ + 3y = 35}$ ${y = 10}$